This retrospective, descriptive, observational study used routinely collected patient data from the Inselspital University Hospital, Bern, Switzerland. As one of Switzerland’s five University Hospitals, the Inselspital treats approximately 48,000 inpatients annually [26]. Only inpatient units with data for the full 3 years were included. Our data were drawn from 10 departments: (1) Internal Medicine; (2) Cardiology & Cardiovascular Surgery; (3) Orthopedics & Plastic Surgery; (4) Neurology, Neurosurgery, Otolaryngology, Head and Neck Surgery, & Ophthalmology; (5) Visceral Surgery and Medicine, Gastroenterology, Thoracic Surgery, & Pulmonology; (6) Dermatology, Urology, Rheumatology, & Nephrology; (7) Hematology & Oncology; (8) Maternity & Gynecology; (9) Pediatrics; and (10) Intensive Care. Full data (2015–2017) were available for all these departments for the full study period.

We extracted our data from two sources: the tacs nurse staffing system (ie, datasheets organized in a relational database) and medical discharges. From tacs, we extracted four care-relevant factors: nurses, patients, activities, and care-related working hours. The tacs system records time allocations provided by every nurse at the end of every shift. In addition to administrative work, teaching duties, and continuous education, each record specifies the time devoted to each patient’s direct and indirect care. No further details about the type of activity such as medication, mobility, or respiratory therapy are currently available. Nurses’ absences such as holidays, illnesses, or accidents are also recorded. Patient turnover information is provided with the nursing unit, date, and time, as well as whether inpatient or outpatient services were provided. Finally, medical discharge data include patient demographics, admission and discharge details, and diagnoses. Each data record identifies the relevant unit and includes identifiers for the nurse (and her or his contract) and each case (patient) cared for during that shift. Based on these identifiers, the 5 datasheets were linked at the patient, nurse, and unit levels in a single dataset. Then, all patient, nurse, and unit identifiers were deidentified, leaving only department names. Table 1 describes the 17 variables used in the analysis.

All statistical analyses were conducted using R, version 3.5.1 for Mac OS and Linux [27]. To handle and manipulate the data, we used the purrr [28], dplyr [29], tidyr [30], and data.table [31] packages. To manipulate time and date, we used the lubridate [32], chron [33], and padr [34] packages. To create plots, we used the ggplot2 [35] and scales [36] packages.

The main activity data were drawn from 688,730 cases and 6834 nurses in 152 units. After the exclusion of outpatient units and noncare activities (whether direct or indirect), the activity data reflected 153,456 cases (153,456/688,730, 22.2%) and 5736 nurses (5736/6834, 83.9%) in 70 units (70/152, 46.1%). Of the remaining 5736 nurses, data from 4633 (80.8%) were usable for the final analyses. A number of nurses (1270) were excluded for specific days only, as they had recorded no working time data. Those exclusions correspond to 11,251 (1.5%) person-days. Another main reason for exclusion was that 1109 students and 227 external nurses did not have exact working hours. However, the data from both groups were usable for our descriptive analyses. Numerous students and external nurses became RNs over the 3 years of the study period. This largely explains why the final number of nurses was higher than 5736. Regarding the number of cases, a total of 128,484 (124,484/153,456, 83.7%) cases were used. Two main factors explain this reduction: outpatients (19,442/153,456, 12.7%) and healthy newborn babies (3779/153,456, 2.5%) from the Maternity & Gynecology department. Further details of the linking procedure are shown in Figure 1. For patient-to-nurse ratios and patient turnover analyses, we included 10 departments, including 70 inpatient units in which 4633 nurses (>22 million data points) provided care to 128,484 cases (>35 million data points).

The number of patient cases in the included units in each department over the study period (2015-2017) ranged from 5007 for Hematology & Oncology to 28,377 for Cardiology & Cardiovascular Surgery. In almost all departments, mean and median patient ages were >54 years. The exceptions were patients in Maternity & Gynecology, who had a mean age of 36.5 years (SD 15.4 years) and median age of 33 years (IQR 28-40 years), and in Pediatrics, who had mean and median ages of 3.8 years (SD 5 years) and 1 year (IQR 0-7 years), respectively. The Hematology & Oncology, Internal Medicine, and Orthopedics & Plastic Surgery departments had the highest median LOS, at 7 days (IQR 4-14 days), 6 days (IQR 3-10 days), and 5 days (IQR 3-9 days), respectively. Cardiology & Cardiovascular Surgery and Intensive Care had the lowest median LOS, at 2 days (IQR 1-7 days) and 2 days (IQR 2-3 days), respectively. The most common diagnoses were tumors, predominantly in the Hematology & Oncology department (4161/5007, 83.1%); circulatory system diseases, mainly in the Cardiology & Cardiovascular Surgery department (24,206/28,377, 85.3%); and traumatic injuries, poisonings, and other consequences of external causes, which were highest in the Orthopedics & Surgery department (5213/10,489, 49.7%). Further details are provided in Table 2.

Numbers of patients and nurses and patient-to-nurse ratios were plotted against the 48 data points per day for each day of the week, each of the 10 departments, and each of the 3 nurse groups. Considering the large number of plots this generated, we show only the 3 plots that show the key characteristic patterns: the RN group (group 1) for the Intensive Care, Maternity & Gynecology, and Internal Medicine departments (see Figure 2). All plots can be found in Multimedia Appendix 1 (group 1, RNs), Multimedia Appendix 2 (group 2, LPNs), and Multimedia Appendix 3 (group 3, others).

On the demand side, a number of broad patterns emerged, several of which occurred across departments. Demand fluctuated not only throughout the day, with various clear peaks, but also through the week, as shown for the Maternity & Gynecology department, where patient numbers peaked on Thursday and Friday. Overall, patient numbers increased for 6 departments (6/10, 60%) from Monday to Thursday or Friday, and patient numbers peaked daily between 8:00 am and 10:00 am, then either stabilized or decreased. On Friday mornings, patient numbers decreased in preparation for the weekend. The exception was in the Internal Medicine department, where the number of patients increased continuously from Friday evening until Monday morning (see Figure 2).

From the care supply perspective, variation was far less pronounced than on the demand side. Three main variations were apparent. First, fewer nurses were present through the weekends and occasionally on Friday. Second, Sundays generally had fewer nurses than on Saturdays. Third, the numbers of nurses were highest in the morning, then dropped for the afternoon shift and again for the night shifts. These patterns where quite stable throughout the week. In 6 (6/10, 60%) of the departments, gaps of 1 or 2 nurses were clearly discernible between 11:00 am and 1:00 pm.

Except for 3 (30%) of the 10 departments with almost no staff on the weekends, 1-2 LPNs were mainly present between 06:00 am and 5:00 pm. The pattern for nurse group 3 (ie, others) was similar to that of LPNs, although generally with roughly 1 more care staff. All departments increased their staff by 1-3 nurses for all or several of the following times: 7:00 am to 8:00 am, 2:00 pm to 4:30 pm, and 10:00 pm to 12:00 am (see Figure 2). As mentioned, apart from daily information, no records of working time were available for either students or external nurses. For external nurses and students, the median daily number of nurses was 0, except in the Internal Medicine department, where there was a median of 1 student. The daily number of external nurses ranged from 0 to 9 and of students from 0 to 12. For both, the maxima occurred only once, on a Sunday, during the 3 years.

Figure 2 shows the plots, and Figure 3 shows the median (IQR) of the patient-to-RN ratio for 3 key time points on weekdays and weekends. For RNs, the ratio was highest at night and lowest in the morning. During the night, the median ratio was 4-11 patients per RN, except in the Intensive Care department, which had a ratio of 1.1 patients per RN. In the morning, the ratio ranged from 0.6 (IQR 0.4-0.8) on weekdays to 0.8 (IQR 0.6-1) on weekends in the Intensive Care department and ranged from 2.8 (IQR 2-3.5) on weekdays to 4 (IQR 3-5) on weekends in the Maternity & Gynecology department. For LPNs, the median number was always 0 (IQR 0-0) at night, while the median number in the morning ranged from 3 to 8. For nurse group 3 (ie, others), a median number of 0 (IQR 0-0) staff members was generally present during the night shift. In the morning shifts, 7 departments’ (7/10, 70%) median patient-to-nurse ratios increased for group 3 (ie, others) from weekdays (4.3 to 8) to weekends (6 to 12). In the afternoon shifts, all medians decreased (see Multimedia Appendix 4).

Figure 3 shows not only the weekday and weekend medians (IQRs) of the patient-to-RN ratios for 3 key time points (namely 2 am, 10 am, and 6 pm) but also the threshold values and percentages of shifts with extreme supply-and-demand mismatches. Complete results can be found in Multimedia Appendix 4. For 7 departments (7/10, 70%), the percentages of shifts with extreme staffing increased from morning to night and from weekdays to weekends. For RNs, the lowest percentages of extreme understaffing and overstaffing happened on 2.5% and 0.1% of weekday and weekend mornings, respectively. For both extremely high and extremely low patient-to-nurse ratios, the highest incidence (around 30% of shifts) occurred in the evening and weekend nights. These ratios occurred in the Cardiology & Cardiovascular Surgery (lower); Dermatology, Urology, Rheumatology, & Nephrology (lower); and Hematology & Oncology (higher) departments. The same 3 departments had the lowest incidence of shifts with “normal” staffing levels (below 55%) for weekend nights. On the other hand, more than 80% of all shifts in the Orthopedics & Plastic Surgery department fell within “normal” staffing levels. For nurse groups 2 (LPNs) and 3 (others), the incidence of extreme staffing ranged from very high (49.5%) to very low (1.5%) to none (0%). Possibly because of these groups’ low nurse numbers, no clear patterns were apparent.

Similar to the patient-to-nurse ratio, bar charts for patient turnover are displayed for only the Intensive Care, Internal Medicine, and Maternity & Gynecology departments (see Figure 4). Bar charts for all 10 departments are displayed in Multimedia Appendix 5. All departments showed reductions in patient turnover during the weekends. Entries (admissions and transfers in) and exits (discharges and transfers out) of patients occurred at very similar times for all departments: 09:00 am to 11:00 am and 1:00 pm to 3:00 pm. The Intensive Care department had the highest percentage of transfers (peaking at almost 13% at 9:30 am). As shown in Figure 3, the numbers of extreme staffing mismatches also fluctuated as a result of the number of either nurses or patients present. Figure 4 shows the variation in the patterns throughout the day that influenced the patient-to-nurse ratio. For example, if on a given day a peak of discharges occurs at 10:00 am with no or few admissions or transfers in, the patient-to-nurse ratio will decrease, potentially leading to extreme overstaffing. The same is true for the inverse. A peak in admissions or transfers in can increase the patient-to-nurse ratio, leading to extreme understaffing.

For the first time, we longitudinally analyzed demand for and supply of care at 30-minute intervals for 24 hours a day over a period of 3 years in a large university hospital. Data from the nurse staffing system (tacs) and medical discharge records were used to explore patient-to-nurse ratios and patient turnover. The 10 departments belonged to the Inselspital (Bern University Hospital) and varied by purpose, size, number of units, and patient population.

From the demand side, continuous turnover meant patient numbers fluctuated across each day and varied across units. Less variation was seen in the supply side, where the change in the number of nurses occurred mainly for each shift (night, morning, evening). RNs accounted for roughly three-quarters of the nurse workforce, making them the largest staff subgroup involved with patient care. The remaining quarter was comprised of others (including unlicensed personnel and administrative staff) and LPNs. These smaller groups were mainly present during day shifts on weekdays.

Simultaneous longitudinal data on patient and nurse numbers allowed us to determine which had the greater influence on patient-to-nurse ratios (ie, the effects the variations in the numbers of nurses and patients had on nurse workload). Most published studies have shown that during weekends, patient-to-nurse ratios tend to increase [6,7]. We confirmed this observation, not only because the nursing staff was reduced over weekends but also because in many departments (eg, Internal Medicine), patient numbers tended to increase on Saturday and Sunday. In fact, we found that the supply side remained quite constant; it was mainly the demand side that drove patient-to-nurse ratios.

The ramifications of a demand-driven workload are particularly clear regarding weekend staff planning. Reducing staffing for reduced weekend demand might be justified on Friday nights, as a surge in discharges Thursday and Friday decreases patient numbers. However, patient numbers increased in several departments over the weekends, as patient entries outnumbered exits.

To set the reported patient-to-nurse ratios in context, the European cross-sectional study RN4CAST, which was conducted in 2009-2011 with 35 Swiss acute care hospitals, reported an average of 7.9 patients per nurse in medical and surgical units [37,38]. However, the reported ratios were aggregated at the hospital level, ignoring the ratios per shift. In 2015, the Swiss cross-sectional Match^RN study followed up the same hospitals that participated in RN4CAST [39]. The overall average patient-to-nurse ratio of the 23 participating hospitals was 7.8, and the shift averages were 5.9 for the morning shift, 7.3 for the evening shift, and 14.2 for the night shift [40,41]. Both cross-sectional studies surveyed only RNs. From our study, the median patient-to-nurse ratio for RNs was 2-3 for the morning shift, 3-5 for the evening shift, and 4-10 for the night shift, excluding the Pediatrics, Maternity & Gynecology, and Intensive Care departments. The ratios are difficult to compare with the overall averages from the RN4CAST and Match^RN studies. At the shift level, our patient-to-nurse ratios were lower than the Match^RN ratios, suggesting an above-average staffed hospital. High patient-to-nurse ratios have been associated with worse patient outcomes; however, due to conflicting results, the relationship remains unclear [42,43]. One main reason for the lack of conclusive evidence is researchers’ tendency to seek associations between mean patient-to-nurse ratios and patient outcomes [44]. However, this means obscuring sharp changes in supply and demand, thereby concealing periods when staffing levels are low. As no consensus exists concerning the definition of an extreme staffing situation, we chose arbitrary cut-offs of double or half of the median work per nurse to define extremely high or low patient-to-nurse ratios, respectively. These cut-offs showed that our extreme thresholds were commonly crossed during certain shifts and in certain departments.

This observation underscores the potential volatility of nurse workload, even over a single shift, and the need for longitudinal approaches to staffing research to help identify and counteract this volatility [45]. The distribution of extreme shifts also indicated that individual departments (eg, the Orthopedics & Surgery department, with more than 80% of units and shifts staffed within the “normal” range) can maintain their patient-to-nurse ratio quite effectively. Identifying the most meaningful thresholds to define extreme staffing will require further research.

As illustrated in Figure 4, while patient turnover was continuous, it was concentrated at various times throughout the day. Consistent with previous findings, entries and exits were both rare during the night [46,47]. Moving patients to the units where they can receive the most appropriate care is essential for their recovery. Also, as demand is independent of available resources, patient turnover occurs when units are short on either staff or beds. For the former, the unit is closed, and the patient is moved to a similar unit; for the latter, the patient is placed in an intermediate unit until a bed becomes available [48]. However, both cases lead to increased administrative work, and even where beds are available and staff sufficient, transfers, admissions, and discharges all entail higher volumes of administrative requirements and patient care needs. Therefore, our analyses confirmed that patient turnover is one factor for nursing workload [5,47,49].

The impact of turnover can be greater when entries and exits occur at the same time, as illustrated in the first row of Figure 4 for the Intensive Care department. Between 1.6% and 32.3% of nursing time is spent on patient turnover-related activities [50,51]. Associations between patient turnover and nursing care quality have been documented, where higher turnover led to higher nursing workload, possibly compromising nursing care quality [13,38,52]. High patient turnover is associated with more adverse events, including mortality [53], nosocomial infections [54], and medication errors [52] as well as more readmissions [55,56]. The current approach is somewhat unrealistic. Where each patient case or event is rooted in a unique context, much of the current literature treats all patient turnover and patients as the same [47,57]. In contrast, Tierney et al [58] used weighted patient acuity and patient turnover variables to account for intercase variation. Studies also showed that death was a more likely outcome in contexts featuring high patient-to-nurse ratios and patient turnover [13,59,60].

Because of the granularity of the analysis, patient-to-nurse ratios were analyzed with patient turnover, as even in cases where the patient-to-nurse ratio might appear normal, both patient entries and exits increase nurse workload. During periods of high turnover, the time available for patient care can be severely reduced. Hospitals or departments that fail to account for this additional burden commonly operate with suboptimal nursing staff levels [51-53].

Previous research has suggested a relationship between higher patient-to-nurse ratios and worse patient outcomes [61-66]. Mandatory minimum patient-to-nurse ratios are often suggested as an approach to ensure safe staffing levels. As the nursing supply is quite constant at the level of individual shifts, the question may arise as to whether that supply can realistically be changed in response to midshift fluctuations in demand. The patient turnover variability illustrated in this study showed that where entries matched exits, patient numbers remained reasonably constant and where imbalances occurred between entries and exits, patient numbers fluctuated.

However, neither of these cases adequately reflects nurse workload. In the first, even while a balanced turnover resulted in a constant patient-to-nurse ratio, if both sides increased, the additional work required for each incoming and outgoing case would represent a considerable burden. In the second, records of patient numbers alone give no indication as to whether the supply of nurses was adjusted accordingly. These two examples illustrate the necessity of considering both supply and demand data for staffing purposes.

Certain patterns were clearly associated with routines that applied to specific days and times of the week. Defining and clarifying those periods for each unit would help improve assessment of staffing levels. Given that some hospital departments do not operate on the weekends, further detailed analysis of weekend work for nurses is needed to determine how the workload increases. Current research on hospital staffing is predominantly based on cross-sectional data, which cannot show fluctuations in patient turnover [67]. Lacking longitudinal data, it is extremely difficult to match the rather constant nurse supply to the varying patterns in patient demand.

To our knowledge, only one previous study examined the longitudinal associations between nurse staffing and patient turnover. Its findings indicated large variations in patient turnover [68]. As the demand side is quite volatile, to anticipate when the nurse supply should be changed to match changes in workload, it is important to identify the times of day, days of the week, and even months during which specific entry and exit patterns occur. Armed with this information, staffing levels might differ across not only units and hospitals but also countries. Thus, unit-level analysis offers the best chance to detect patterns of supply and demand. Identifying the complex relationships involved and then building more efficient predictive models that capture all meaningful variations will require further studies examining longitudinal nurse and patient data.

Certain limitations were encountered during our analyses. One of these concerned the tacs nurse staffing system, as this was the first time that routine data were used for research and linking purposes. During the process, we found that a small minority of nurses (~ 1%) were not using the system consistently. Also, due to issues with merging data, a number of nurses and patients were excluded from the analysis. To maximize the data quality for this and future studies, these issues were discussed with the nurse staffing system software developers.

Also, while we selected persons providing direct or indirect care for the analysis, it was impossible to know whether those people also performed tasks not associated with patient care, such as organizational tasks or teaching. Patient-to-nurse ratios were calculated for all persons present in each unit studied. Although we measured variation in nurses’ workload with a high level of granularity, the significance of the short peaks in demand relative to the supply over short periods is hard to judge because nurses’ work involves multitasking and they can prioritize urgent tasks and delay others without necessarily harming patients [69]. Minutes of care were also available from the data; however, due to data quality concerns regarding the time allocated to each patient, these data were excluded, and metadata were included in their place. This may have solved the patient care time data limitation by providing the exact time invested for each patient during working hours.

Further, the results were limited by the absence of accurate working time data for external nurses and students. Even if these groups had a daily median presence of 0, their assistance might have been crucial when they were present, as for night shift support. This type of task shifting between individuals and departments to compensate for staffing shortfalls is a key tool to handle demand and avoid gaps in supply but was not recorded in the available data.

Our study looked only at nurses, but the hospital environment is multidisciplinary. All health care providers play an important role, and their collaboration is crucial for patients [70]. For example, studies showed a positive impact on patients’ outcomes by incorporating or improving nurse-physician or pharmacist-physician collaborative practices [71-73].

Finally, the study was undertaken in a single hospital, and we explored many sources of variation, but not patient acuity and severity. Nursing workload depends on not only the amount of direct and indirect care, patient turnover, and patient-to-nurse ratio but also patient acuity and severity [74,75]. Further investigation is thus needed.

To our knowledge, this is the first detailed study to use data on patient-to-nurse ratios and patient turnover in time increments as low as 30 minutes. The goal was to illustrate fluctuations in these two variables between and within departments and days of the week. The choice of 30 minutes was subjective and based on available computational resources. While the literature includes references to the fluctuations we observed, no study to date has illustrated those fluctuations in such fine detail. The key driver for care was clearly patient demand, which showed high variability even during individual shifts. This volatility challenges health care suppliers to provide safe and reliable care when demand is high while avoiding overstaffing when it is low. Detecting patterns of variation will help optimize staffing. This descriptive analysis was a first step towards detecting fluid variables to be considered in developing a predictive model on which to base health care staff planning, possibly including the introduction of innovative working/shift schemes in this sensitive sector.